What is the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10?

How many ways are there to rearrange the letters ALIVE in such a way that the word EVIL is not contained in the resulting word

Sergio [31]

Answer: 118 combinations.

Step-by-step explanation:

In ALIVE we have 5 letters, rearranging it we have the possible options of:

5 options for the first letter.

4 options for the second letter, as one was already chosen for the first one

3 options for the third letter, as 2 were already chosen.

2 options for the fourth letter.

1 option for the last letter.

The total number of combinations will be equal to the product of the numbers of options for each letter, then we have:

5*4*3*2*1 = 120 combinations.

And the combinations where the word EVIL is formed are:

AEVIL

EVILA

2 combinations, then the total number of combinations such that the word evil is not formed are:

120 - 2 = 118 combinations.

5 0

2 years ago

Solve the system of equations. y= x + 17, y= 3x+1

Lemur [1.5K]

Answer:

x=8, y=25. As a point it's (8,25)

Step-by-step explanation:

here is the system:

y=x+17

y=3x+1

notice how both of the equations equal y. Therefore, we can substitute one expression as y in the other expression. (It'll equal y=y, which is a true statement)

so it'll be:

3x+1=x+17

subtract 1 from both sides

3x=x+16

subtract x from both sides

2x=16

divide by 2

x=8

now, substitute 8 as x into one of the equations and solve for y

let's take the first one for example

y=8+17

y=25

so the answer is x=8, y=25. As a point it's (8,25)

Hope this helps!

7 0

3 years ago

Factor the polynomial.

Degger [83]

It is answer choice A because you have to take the the GCF of each number which is 2x. Then if you were to divide the numbers by 2x you would put those numbers in the brackets.
$2x( x^{2} +2x+4)$ because $2x^3/2 x = x^{2}$ and $4 x^{2} /2x = 2x$ and $8x/2x = 4$

8 0

3 years ago

Read 2 more answers

5(y+2)= -3 Whats the answer TvT

Iteru [2.4K]

Answer:

The answer is given below

Step-by-step explanation:

$(5y + 10) = - 3$